Based  on Chapters 4  of Berenson et  al.  (2019), Basic Business Statistics:  Concepts and Applications, 5th Edition, Frenchs forest, N.S.W.: Pearson Australia

A. MCQs

1.   A numerical value representing the chance, likelihood, or possibility that a particular event will occur

a.   Event

b.   Probability

c.   Simple event

d.   Complement event

2.   An event that has no chance of occurring

a.   Probability

b.   Certain event

c.   Impossible event

d.  None

3.   Imagine rolling a six sided die, the sample space is

a.   {1, 2, 3, 4}

b.   {1, 2, 3, 4, 6}

c.   {1, 2, 3, 4, 5, 6}

d.   {1, 2}

4.   A subset of sample space to which a probability is assigned

a.   Complement

b.   Experiment

c.   Event

d.  None

5.   When you toss a coin, the two possible outcomes are head and tail. Each of these represents

a.   A joint event

b.   A simple event

c.   Sample space

d.   a and c

6.   Getting two heads when you toss a coin twice is an example of

a.   A simple event

b.   Sample space

c.   Joint event

d.  b and c

7.   Given the probability of an event, the probability of its complement can be found by subtracting the given probability from 1

a.   False

b.   Cannot be determined from the information given

c.   True

8.   If A and B are mutually exclusive, then the P(A and B) is equal to

a.   0

b.   1

c.   0.5

d.   0.75

9.   Consider the experiment of flipping a coin. Which statement is true?

a.   Events can be mutually exclusive but not collectively exhaustive

b.    Events can be collectively exhaustive but not mutually exclusive

c.   Cannot be determined from the information given

d.   Events can be mutually exclusive and collectively exhaustive

10. Independent events can happen when

a.   The two events are unrelated

b.   You repeat an event with an item whose numbers will not change

c.   You repeat the same activity, but you replace the item that was removed

d.   a, b and c

Questions requiring numerical/written answers

11. Consider a deck of playing cards. Assume A = aces; B = black cards; C = diamonds; D = hearts. For each of the following, state whether the events are mutually exclusive and collectively exhaustive

a.   Events A, B, C and D

b.   Events B, C and D

12.

Use the above information to calculate the probability of each of the following and decide whether it is simple or joint or conditional probability

a.   A1

b.   A2

c.   B1

d.   B2

e.   A1 and B1

f.   A1 and B2

g.   A2 and B1

h.   A2 and B2

i.   B1 | A1

13. For the above example find

a.   P(A1 or B1)

b.   P(A1 or B2)

14. A sample of 500 purchasing managers was selected across Australia to determine information concerning buying behaviour. Among the questions asked was, ‘Do you enjoy your role in the  organisation?’  Of 240 males,  136  answered YES.  Of 260 females, 224 answered YES.

a.   Construct a contingency table

b.   What is the probability that a respondent chosen at random enjoys his/her role in the organisation?

c.    What is the probability that a respondent chosen at random is a female and enjoys her role in the organisation?

d.   What is the probability that a respondent chosen at random is a female or enjoys her/his role in the organisation?

e.   What is the probability that a respondent chosen at random is a male or a female?

15. A card is drawn randomly from a deck of 52 ordinary playing cards. You win $10 if the card is a spade or an ace. What is the probability that you will win the game?

16. What is the probability that two tails occurs when two coins are tossed?

17. The  probability  that  a  regularly  scheduled  flight  departs  on  time  is  0.83,  the probability that it arrives on time is 0.92, and the probability that it departs and arrives on time is 0.78. Find the probability that a plane (a) arrives on time given that it departed on time, and (b) departed on time given that it has arrived on time?

18. At a school, the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68. What is the probability that a student takes Spanish given that the student is taking Technology?

19. From 4 Labours and 3 Liberals find the number of committees of 3 can be formed with 2 Labours and 1 Liberal